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Metaheuristic optimization algorithms play a crucial role in optimization problems. However, the traditional identification methods have the following problems: (1) difficulties in nonlinear data processing; (2) high error rates caused by local stagnation; and (3) low classification rates resulting from premature convergence. This paper proposed a variant based on the gray wolf optimization algorithm (GWO) with chaotic disturbance, candidate migration, and attacking mechanisms, naming it the enhanced gray wolf optimizer (EGWO), to solve the problem of premature convergence and local stagnation. The performance of the EGWO was tested on IEEE CEC 2014 benchmark functions, and the results of the EGWO were compared with the performance of three GWO variants, five traditional and popular algorithms, and six recent algorithms. In addition, EGWO optimized the weights and biases of a multi-layer perceptron (MLP) and proposed an EGWO-MLP disease identification model; the model was tested on IEEE CEC 2014 benchmark functions, and EGWO-MLP was verified by UCI dataset including Tic-Tac-Toe, Heart, XOR, and Balloon datasets. The experimental results demonstrate that the proposed EGWO-MLP model can effectively avoid local optimization problems and premature convergence and provide a quasi-optimal solution for the optimization problem. [ABSTRACT FROM AUTHOR]